1 Introduction

Intense typhoons can cause storm surges that run up in rivers and overflow riverbanks, resulting in inundation. Such flooding can be exacerbated when the storm surge runup coincides with peak river flows due to heavy precipitation. The simultaneous occurrence of two hazards is inferred to lead to compound floods (Wahl et al. 2015; Sebastian et al. 2021; IPCC 2021). Wahl et al. (2015) investigated the co-dependence of storm surges and heavy precipitation and reported that they have become more correlated with time. These results suggest that a strong tropical cyclone may cause simultaneous storm surge and flooding in coastal areas. Sebastian et al. (2021) pointed out that conventional risk assessments (separate analysis of storm surge and river flood) cannot adequately qualify the precipitation and storm surge-induced compound flood and may underestimate the damage they cause. The analyses of storm surge and high river flows separately underestimated the interaction among them and failed to accurately account for water level rise. The Intergovernmental Panel on Climate Change AR6 (IPCC 2021) also highlights the urgent need for countermeasures against compound flooding.

The Northwest Pacific Ocean is one of the most active areas for typhoons. Since 1991, the yearly number of typhoons making landfall in Japan and that approaching 300 km off Japan is 3.0 and 11.7 on average, respectively, according to Japan Meteorological Agency (JMA). Among the historical typhoons, Typhoon Jebi in 2018 generated a record-breaking 3.29 m storm surge height in the Osaka Bay area, followed by Typhoon Nancy (1961) at a surge height of 2.93 m in the Bay (Mori et al. 2019). Mori et al. (2019) reported that Typhoon Jebi produced multiple hazards-induced floods, including wave overtopping/runup, river overflow, surge overflow, surge runup in rivers, sewer backflow, and high wave. The Jebi-induced surge ran up the Yodogawa River. A major flooding would have occurred if the water level had been 1 m higher. This event clearly demonstrates the compound flood risk of the storm surge and river flow in Osaka Bay (JMA 2018; Mori et al. 2019). Although compound flooding by storm surge and river flow has not yet occurred, Typhoons Faxai and Hagibis in 2019 caused serious disasters in Japan (Shimozono et al. 2020; Suzuki et al. 2020). In particular, Faxai induced a record-breaking storm disaster that occurred mainly in the Chiba Prefecture, causing a large-scale power outage (JMA 2019). Furthermore, flood damage due to waves and storm surges occurred in the coastal area of Kanagawa Prefecture. Meanwhile, Hagibis recorded the highest historical total precipitation at 613 locations in northern and eastern Japan (JMA 2019). The Hagibis-induced storm surge and wave inundated coastal areas and caused roads to be sunk in the Shizuoka Prefecture. Strong typhoons have sequentially struck Japan in recent years, which is expected to increase the risk of compound flooding. Typhoons that have struck Japan within the past 5 years have caused severe storm surges or floods (Mori et al. 2019; Suzuki et al. 2020; Shimozono et al. 2020). Typhoon disasters are becoming more serious, and compound floods may occur anytime. In addition, Japan is considered to have a high risk of compound flood owing to its topographical characteristics. Rivers in Japan have an extremely high river regime coefficient owing to their steep topography and are characterized by a rapid rise in water level owing to precipitation associated with typhoons (JMA 2017). Furthermore, the three major bays (namely the Ise, Tokyo, and Osaka Bays) have the potential for large-scale storm surges (e.g., more than 3 m) because of their shallow terrains. The topographic features of shallow water and an open bay mouth to the south tend to cause large storm surges associated with typhoons. The averaged water depths of the major three bays in Japan are 15 m (Ise), 15 m (Tokyo), and 30 m (Osaka), and the areas were 2100 km2 (Ise), 1400 km2 (Tokyo), and 1500 km2 (Osaka). The highest storm surge heights in each bay (JMA https://www.data.jma.go.jp/gmd/kaiyou/db/tide/list2.html) are 2.03 m (Tokyo, Typhoon Tip; 1979), 3.89 m (Ise, Typhoon Vera; 1959), and 3.29 m (Osaka, Typhoon Jebi; 2018), respectively. Moreover, because various small- and medium-sized rivers go through residential areas, the water level change and warning are critical issues for vulnerability to typhoons (JMA 2017).

Several studies on compound floods have been published (e.g., Ikeuchi et al. 2017; Kumbier et al. 2018; Pasquier et al. 2019; Hendry et al. 2019; Yin et al. 2021; Toyoda et al. 2021). For example, Ikeuchi et al. (2017) conducted a flood simulation to investigate the simultaneous occurrence of storm surges and river flows in Bangladesh during Cyclone Sidr. They reported that the storm surge and high river flow induced-inundation depth in the estuary increased by more than 3 m compared to the inland flood induced only river flooding. In addition, the compound flood resulted in an inundation depth 0.7 m higher in the area farther from the estuary. Kumbier et al. (2018) also reported that storm surge and rainfall runoff for inundation evaluation during storms should be simultaneously considered for the 2016 storm event (south-eastern Australia, Shoalhaven estuary), clarifying that the inundation area and depth may be underestimated by approximately 30% (up to 1.5 m) if rainfall-runoff is not considered. Furthermore, Hendry et al. (2019) investigated the influence of catchment characteristics on the potential for fluvial-coastal flooding. They reported that the basin with a lower base flow index and steeper elevation gradient has a high risk of skew surges with high river discharge in the UK. Toyoda et al. (2021) studied Typhoon Jebi (2018), which caused a severe storm surge runup at the Yodogawa River in Osaka Bay, Japan. They reported that it is essential to consider the impact of the storm surge runup in the river to evaluate Jebi-induced and -combined inundation due to storm surges and river flow using a coupled surge and wave model and a regional climate model that considers a storm surge runup in rivers.

However, these studies used insufficient methods in physics for the coastal area and ignored the effect of the wave on the sea surface level and that of the topography on the meteorological field, focusing only on large rivers (i.e., river lengths of more than 50 km). In other words, the potential risk of the small- and medium-sized rivers (river length of less than 50 km or river width of less than 100 m) was not investigated in detail. Furthermore, several studies (e.g., Mori et al. 2019; Yin et al. 2021) investigated the protection level of a large-scale river that is sufficiently set high, and severe floods in the large river are unlikely to occur, except in extreme events. Small and medium-sized rivers have lower protection level than large-scale rivers generally. It is necessary to understand such compound floods in small and medium-sized rivers.

Therefore, this study aimed to quantitatively evaluate the impact of compound occurrence of storm surge and river flood during typhoons in the Ise and Mikawa Bays in Japan (Fig. 1a). To achieve this, first, we developed a framework (Sect. 2) of surge, wave, precipitation, river flow, and wind and pressure using a coupled model of tide, surge, and wave (SuWAT); dynamical meteorological model (WRF/HTM); and rainfall-runoff-inundation model (RRI). The typhoon meteorological field was simulated by the dynamical meteorological model, and rainfall-runoff by RRI, and these results were input to SuWAT to evaluate compound floods. The framework of the integrated atmosphere–ocean-river model was used to simulate river flows in 11 rivers (five large-scale rivers and six small and medium-sized rivers). Many recent studies have used numerical models in combination with statistical models (e.g., Bilskie et al. 2018; Moftakhari et al. 2019; Jane et al. 2022). On the other hand, there are few cases in which the entire sequence of phenomena, rainfall-runoff, river discharge, and storm surge, has been evaluated dynamically. Dynamical evaluation is necessary for interacting with coasts and rivers and detecting hazardous areas within rivers. There are also no studies that collectively evaluate the compound flooding risk of rivers of various scales. Then, we conducted hindcast experiments (Sect. 3) for Typhoon Trami (2018) and initial condition sensitivity experiments based on Typhoon Hagibis (2019) to determine the difference between the typhoon track and peak times of storm surges and high river flow (Sect. 4). The sensitivity experimental results from Yoshino et al. (2021) were used for the analysis in Sect. 4. In the sensitivity experiments, typhoons with similar rainfall distribution and intensities were simulated on different tracks to clarify the possibility of the simultaneous occurrence of storm surges and river flows in each river and the difference in characteristics for each river scale. Note that our study focused on the simultaneous occurrence of storm surge and high-river flow.

Fig. 1
figure 1

The simulation areas and list of target rivers for a map of Japan and the target bays, b Ise Bay and c Mikawa Bay, in this study. Red points in the map indicate the gage points of water level. Rivers in yellow in the list are large-scale rivers, whereas the others are small and medium-sized rivers. Light blue areas inland mean zones 0 m above sea level

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2 A framework of atmosphere–river–ocean

A framework of atmosphere–river–ocean was developed by combining a mesoscale meteorological model (weather research and forecasting model, WRF ver. 4.2, Skamarock et al. 2008; high-resolution typhoon model, HTM, Yoshino et al. 2012); rainfall-runoff inundation model (RRI ver.1.4.2, Sayama et al. 2012); and coupled model of surge, wave, and tide (SuWAT ver. 2026A, Kim et al. 2015). The models in the framework were used to accurately hindcast the Typhoon Trami-induced wind and pressure, rainfall-runoff, and storm surges (Fig. 1). The integrated framework simulations have a high computational cost. RRI simulations took several hours for each water system, WRF simulations ~ 5 days per run, and SuWAT ~ 2.5 days per run (used Core i9-10900 K CPU@3.70 GHz). In addition, we are really limited in accessing the number of historical events because of the lack of measurements in medium- and small-sized river basins. Thus, the compound flooding evaluation was performed based on the results of a previous study (Toyoda et al. 2021) for track ensemble sensitivity experiments on Typhoon Hagibis (2019). The sensitivity experiments for storm surge-river discharge based on Typhoon Hagibis were conducted using the results of the typhoon track ensemble experiments by the HTM obtained by Yoshino et al. (2021). The two models of WRF and HTM were used to reproduce the wind and pressure fields induced by Trami and Hagibis, respectively. Section 4 describes the sensitivity experiments in detail.

2.1 Weather, research, and forecasting model (WRF)

The WRF model was used to simulate the meteorological fields of typhoons (Table 1). It is a non-hydrostatic mesoscale model developed by the National Center for Atmospheric Research (NCAR; Skamarock et al. 2008) and is used for a wide range of analyses of tropical cyclones (e.g., Ninomiya et al. 2017). In this study, Typhoon Trami was simulated using reanalysis data (NCEP FNL ds083.3) as input data for WRF. We focused on the reproducibility of the typhoon intensity and track to evaluate the storm surge caused by Typhoon Trami.

Table 1 Computational settings for WRF
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Three nesting domains (D1, D2, and D3) were used as the WRF computational domains: D1 (7.29 km grid) covered almost the entire Japan region, D2 (2.43 km grid) was set up inside D1, and D3 (0.81 km) was set up inside D2. They were used to calculate the meteorological fields of storms at the Ise and Mikawa Bays at a higher resolution. The simulated period was from 0:00 UTC on September 28, 2018, to 0:00 UTC on October 2, 2018 (Sect. 3.1). The initial and boundary conditions were the final analysis data (FNL) of the National Centers for Environmental Prediction (NCEP) on a 0.25-degree grid. High-resolution merged satellite data and in situ data of Global Daily Sea Surface Temperature (HIMSST; JMA 2016) were used as the sea surface temperature (SST) data, which were interpolated every 6 h (original temporal interval was daily, and horizontal resolution was 0.1°). Therefore, the NCEP FNL ds083.3 data were used as the atmospheric field, and HIMSST was used as the SST in this study. Further details of the simulation settings are listed in Table 1.

2.2 A high-resolution typhoon model (HTM)

In sensitivity experiments (Sect. 4.2), the HTM was used to simulate typhoon tracks based on Typhoon Hagibis as the dynamical meteorological model (Table 2). The HTM, a type of regional climate model (RCM), was developed for sensitivity experiments on typhoon tracks (Yoshino et al. 2012, 2015). The HTM is based on the Pennsylvania State University/NCAR fifth-generation mesoscale model (MM5) (Dudhia 1993) and is a three-dimensional, nonhydrostatic, fully compressible, cloud-resolving atmospheric model used to capture mesoscale and local-scale meteorological phenomena. Several types of physical parameterizations were incorporated into the original MM5. Particularly, ocean mixed layers (Shade 1999; Emanuel et al. 2004), dissipative heating (Bister et al. 1998; Zhang et al. 1999), and sea spray processes (Fairall et al. 1994; Wang et al. 2001) have been implemented to express realistic typhoon intensity and structural characteristics accurately. The accuracy of HTM has been confirmed previously (e.g., Toyoda et al. 2022). Toyoda et al. (2022) conducted reproducing experiments for 49 typhoons that made landfall in Japan from 2000 to 2017 and reported that the reproducibility of the HTM was very high and that both weak and strong typhoons could be reproduced.

Table 2 Computational settings for HTM
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Two typhoons, Trami and Hagibis, were considered in the sensitivity experiments. Typhoon Trami has an easterly track and is less likely to cause large storm surges 2 m high in Ise Bay, even when several tracks are considered. Therefore, Hagibis was selected as a case study for the sensitivity experiments because its northerly track causes heavy rainfall and storm surge. Although different typhoon cases were used, both Trami and Hagibis have similar characteristics as they made landfall in Japan with similar intensity (approximately 955 hPa) and took northeasterly paths. In addition, our model can simulate the intensity and meteorological fields. Accuracy validation in previous studies (Yoshino et al. 2021; Toyoda et al. 2022) indicated no significant uncertainty or model bias for typhoon intensity and rainfall owing to the typhoon case used. Thus, we believe our framework with HTM can investigate the impact of the simultaneous occurrence of storm surges and high river flows during typhoons based on the external forcing.

2.3 Computational configuration for rainfall-runoff

A total of 11 rivers were selected as target rivers (Fig. 1). Five were large-scale rivers (> 50 km river length), whereas the remaining six were small- and medium-sized rivers (less than 50 km river length). All river flows were simulated using the rainfall-runoff inundation model (RRI), an integrated 2D hydrological and hydraulic model developed by Sayama et al. (2012) to simulate rainfall–runoff and flood inundation simultaneously (Table 3). The model can simulate discharge using rainfall data. In the RRI model, the flow on the slope grid cells and the river channel are calculated using 2D and 1D wave-diffusive models, respectively. The model also simulates lateral subsurface and vertical infiltration with surface flows.

Table 3 Computational settings for RRI
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Because of the steep slope in mountainous regions, the lateral subsurface flow is particularly important; thus, it was calculated as a discharge-to-hydraulic-gradient relationship. The vertical infiltration flow was estimated using the Green–Ampt model (Rawls et al. 1992). The model to calculate the slope grid cell flow uses mass balance and momentum equations for a gradually varying unsteady flow. The flow in the river grids was calculated using a 1D wave equation. The cross-section of the river was assumed rectangular, with width W, depth D, and embankment height. The width and depth parameters were determined based on the upstream area A (km2) of Eqs. (1) and (2) as below (Sayama et al. 2012):

$$W = C_{w} A^{sw}$$
(1)
$$D = C_{d} A^{sd}$$
(2)

where \({C}_{w}\), \(sw\), \({C}_{d}\) and \(sd\) are regression parameters whose values were estimated from river cross-sectional data (provided by each river administrator). The simulation results of the RRI were sensitive to the cross-sectional parameters of the river. The river width parameters at each estuary site were obtained from Google Earth, and the depth and catchment area were provided by the administrations (Table 4). The Ibi/Nagara Rivers and the Gojo/Shin/Shonai Rivers are located in the same basins; Therefore, similar settings were used for these basins. For the detailed river parameters, the configuration identified from land use data was used (Tables 3 and 4).

Table 4 Parameters for each river used in RRI. The values for river width and river depth represent the mean values of the estuarine grid estimated by Eqs. 1 and 2
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The topographical data input in the RRI simulation included the digital elevation model, flow direction, and flow accumulation pixels obtained from the J-FlwDir (Yamazaki et al. 2018). This database provides data with resolutions of 1 and 3 arcsec. In this study, the three arcsec data were used for large-scale rivers, and the one arcsec data for small- and medium-sized rivers. In addition, land information mesh data (100 m grid) from the Ministry of Land, Infrastructure, Transport and Tourism were used for the distribution of land use (https://nlftp.mlit.go.jp/ksj/index.html). The default land use is classified into 12 types. However, to facilitate the calibration of the parameters, we consolidated them into the five types during the calculation as follows: rice paddy, farmland, mountain, urban, and water area (Konja et al. 2019).

The simulation period in the hindcast experiment in Sect. 3.2 was 17 days, from September 15, 2018, to October 2, 2018. The simulation period in the initial condition of the sensitivity experiments in Sect. 4.2 was 4 days, from October 9–13, 2019. Each simulation has a period for a spin-up calculation of more than 1 day. In the sensitivity experiments for the track estimation, a spin-up is shortly set in a range that does not disrupt the calculation accuracy due to the limitations of the HTM simulation setup.

The eXtended Radar Information Network (XRAIN) was used to estimate precipitation volumes provided by the data integration and analysis system (DIAS), with a resolution of 250 m grid at 10-min intervals. Here, XRAIN rainfall data can be obtained in near real-time with high accuracy and resolution using that X-band MP (multi-parameter) radar. DIAS provides useful information for crisis management against threats, such as global environmental problems and large-scale natural disasters, both domestically and globally (https://diasjp.net/). Although it is possible to obtain precipitation data from the WRF, their time-series values are highly biased by the model. Therefore, XRAIN was used in the hindcast experiments to reproduce the rainfall-runoff with high accuracy. Evapotranspiration was given as an approximate daily average of 2 mm/day in the Chubu region, according to Kobatake (1989). Although this setup is coarse, the current study estimated the total evapotranspiration that is less than 5% of the total rainfall estimated. Therefore, the values do not significantly affect the calculation results.

2.4 Computational configuration for surge-wave coupling model

The storm surge was calculated using the coupled model of surge, wave, and tide (SuWAT) developed by Kim et al. (2015). The SuWAT model is based on a nonlinear shallow water equation that considers atmospheric pressure-driven surge, wind stress, and wave radiation stress. Six domains nesting were used with spatial resolutions of 7290 m (D1) to 30 m (D6). The storm surge model considered the wave-induced forces from the radiation stress in the momentum. The calculation domains of D1 to D4 are common, whereas those of D5 and D6 cover the Ise and Mikawa Bays, respectively (see Fig. 1b, c). The bathymetry was grided using the terrain data from the Central Disaster Prevention Council. The 11 river channels were incorporated in the innermost domain to calculate the surge runup in the rivers imposed by river flow rates from the upstream rivers. The simulation period was from 0:00 UTC on September 29, 2018, to 0:00 UTC on October 2, 2018 (Sect. 3.3) and from 0:00 UTC on October 10, 2019, to 0:00 UTC on October 13, 2019 (Sect. 4.2) for Typhoons Trami and Hagibis, respectively. In addition, a 24-h spin-up calculation was conducted before the main simulation. Wave simulations were not performed during the spin-up period, and water levels and flows were simulated according to the meteorological field. The meteorological field for input was the WRF pressure and wind field output values (10-min intervals), and the RRI output was set as the lateral boundary condition (10-min intervals). The radiation boundary condition proposed by Flather (1994) was applied to the boundary between the RRI and SuWAT following the method of Kim et al. (2011). A seamless connection was achieved by converting the constantly changing discharge calculated from the RRI into the water level according to the river channel topography (river width and water depth) in the SuWAT using Eq. (3) as follows:

$$H_{t} = Q_{t} \times 1/\left( {\Delta t \times W \times D} \right)$$
(3)

where \({H}_{t}\) (m) is the converted water level at time t, \({Q}_{t}\) (m3/s) is the river flow at time t (output from RRI), \(\Delta t\) (sec) is the simulation time step, \(W\) (m) is the river width (30 m multiplying the number of meshes), and \(D\) is the river depth at the boundary mesh. In addition, the coupling between the two models is unidirectional from RRI to SuWAT (one-way). Notably, SuWAT considers the astronomical tide for the hindcast experiments, and we excluded the impact of the astronomical tide for the sensitivity experiments because they are not real cases. The astronomical tide level (Ise Bay and Mikawa Bay) at the time of Typhoon Trami (2018) was approximately 30% of the total water level.

By combining the meteorological, rainfall-runoff, and wave/storm surge models described above, we established an integrated atmosphere–sea–river model to evaluate the precipitation and storm surges associated with typhoons (Fig. 2). Our simulation framework is described as follows. First, the meteorological model was prepared to derive the typhoon meteorological field. Second, each time step of rainfall distribution in the meteorological field was used to simulate the rainfall-runoff using RRI. This process was performed for each watershed. Lastly, the meteorological fields and hydrographs prepared previously were forced to SuWAT as input and boundary values. These three steps comprised the framework to assess the compound flood due to the storm surge and high river flow in coastal urban areas. These models were offline coupled in this study.

Fig. 2
figure 2

Computational flow of hindcast experiments and initial condition of sensitivity experiments. XRAIN was used for precipitation in the hindcast experiment, and HTM output values were used for precipitation in the sensitivity experiments for the typhoon tracks

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2.5 Outline of hindcast and ensemble experiments

Two different simulations were conducted. Sections 3 and 4 describe the numerical experiments in detail. Section 3 first discusses the results of the hindcast experiments for Trami, and Sect. 4 investigates the results of the sensitivity experiments for Hagibis.

Section 3 aims to confirm the validation of the RRI and SuWAT. We used the WRF meteorological field to calculate the wave and storm surge and XRAIN to obtain the time series of precipitation because the WRF-estimated precipitation has a large bias, such as peak time deviations and inconsistency of distribution, and is concerned with a large uncertainty in the RRI. Hence, in Sect. 3, XRAIN was used for precipitation, and in Sect. 4, the HTM results of all meteorological fields (precipitation, pressure, and wind) were used.

Section 4 evaluates the relationship between the typhoon track and the impact of the simultaneous occurrence at the estuary. To the end, the results of sensitivity experiments on typhoon tracks using HTM by Yoshino et al. (2021) were applied. The sensitivity experiments assumed that Typhoon Hagibis passes Ise Bay and Mikawa Bay with various tracks. Hence, observation data such as XRAIN cannot be used in terms of reproducibility of topographic precipitation when assuming a typhoon track that differs from a real track. Therefore, all meteorological fields must be simulated by a meteorological model. Previous studies (Yoshino et al. 2021; Toyoda et al. 2022) confirmed that HTM could accurately represent precipitation distribution, pressure, and wind fields. Therefore, the model bias was considered small, and the simulated results can be used as input values for RRI and SuWAT.

3 Results of hindcast experiments

This section reports the hindcast results of the meteorological field, river discharge, and storm surge in Ise Bay and Mikawa Bay during Typhoon Trami.

3.1 Validation of meteorological fields

First, we confirmed the reproducibility of the typhoon intensity and track using WRF (Figs. 3 and 4). There were no significant differences between the simulated track in black in Fig. 3 and the JMA best track in red, indicating that the typhoon track could be accurately reproduced. The WRF model well simulated Trami’s central pressure at each time in the best track. The simulated central pressure was 962.3 hPa at landfall, while the observed value was 960 hPa.

Fig. 3
figure 3

Results of Trami’s track (lines) and central pressure (colors) based on hindcast experiments. The red dotted line (triangle) indicates JMA best track data, and the black solid line (circle) represents a result of WRF. The color bar and each plot color indicate a central pressure for each time step

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Fig. 4
figure 4

Scatter plot between the observed and estimated wind speeds for half a day based on hindcast experiments of Trami. Each symbol indicates each observation site

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Next, we compared the simulated wind speed half a day before and after the typhoon’s closest approach to the six anemometer observations by the JMA (Fig. 4) installed along the Ise and Mikawa Bays. Although there were variations along the stations, the model results showed trends revealing wind speeds > 20 m/s at sites near the typhoon center and wind speeds of ≤ 5 m/s at sites far from the typhoon core. Both strong and weak winds were represented with high accuracy. The bias error was 1.04 m/s, the root mean square error was as small as 3.56 m/s, and the correlation coefficient was as high as 0.78. Thus, the reproducibility of the typhoon meteorological field by the WRF was high.

3.2 Validation of rainfall runoff and river discharge

In the 11 river targets in this study, the simulated peak river discharges of five rivers (Ibi River, Nagara River, Kiso River, Shonai River, and Toyo River) were validated with the observed values (Table 5 and Fig. 5). The river discharge observation is conducted only in large-scale rivers by the river administrator. Thus, discharge validation was conducted for the five rivers. The observation stations are Mangoku (Ibi River), Sunomata (Nagara River), Okoshi (Kiso River), Biwajima (Shonai River), and Tougo (Toyo River). The river discharge peaked after the passage of the typhoon in all five rivers. All these rivers are large in scale (river length ≥ 50 km) and have large catchment areas (over 700 km2). The Kiso River has the largest catchment area; thus, it reached its peak discharge approximately half a day after the passage of the typhoon. The peak discharges of all rivers estimated by the RRI were relatively close to the observed peak ones. Although the errors were large at the stations of Mangoku (approximately 20%) and Sunomata (approximately 10%) in the same river basin, other rivers could be reproduced with a high accuracy (averaged error: 10.7%). In addition, because the peak times of all rivers well simulated the observation values (error was within 1 h), the accuracy of RRI using XRAIN was judged sufficiently dependable.

Table 5 Results of river discharges at the downstream points of observations and estimations
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Fig. 5
figure 5

Time series of river discharge between the observed (dotted) and estimated (solid) values based on hindcast experiments of Trami. Each color represents one river (green: Ibi, blue: Nagara, yellow: Kiso, light blue: Shonai, and Red: Toyo Rivers)

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3.3 Validation of storm surge at Ise and Mikawa Bays

Based on the simulation results in Sects. 3.1 and 3.2 described above, the SuWAT results are now discussed (Figs. 6 and 7). Figure 6 shows the distribution of the water level deviation (based on Tokyo Peil 0 m) in Ise Bay (Fig. 6a) at 12:30 UTC and in Mikawa Bay (Fig. 6b) at 14:10 UTC on September 30, 2018. In addition, the river water flowing from the boundary to the river mouth can be observed. The peak surge anomalies were approximately 1.4 m and 2.0 m in Ise and Mikawa Bays, respectively. The storm surge anomaly was almost uniform, with no difference between the river mouths.

Fig. 6
figure 6

Distribution of water-level deviations for a Ise Bay and b Mikawa Bay at the peak time of storm surge, as calculated by SuWAT based on hindcast experiments of Trami. The numbers in boxes correspond to Fig. 1

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Fig. 7
figure 7

Time series of water-level deviations at the estuary points for a Ise Bay and b Mikawa Bay. Each solid line indicates the simulation results, while each dashed line indicates the observed results based on hindcast experiments of Trami. In the legend, the rivers that merge at their estuary and flow into the same point are put together. Nikko River is omitted from this figure because the water level gage at its mouth is located inside the sluice gate

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In the time series of the water levels at the estuary of each river (Fig. 7), there was not much error between the simulated (solid line) and observed measurements (dotted line) of the peak values (within 20 cm). Here, the rivers that installed the water level gage at the estuary are indicated in Fig. 7 (some rivers have no measurements). In addition, the observed water levels correspond to the values at 10-min intervals at the river mouth but are not confirmed values. The storm surge peak in Ise Bay was at approximately 12:30 UTC on September 30, and that in Mikawa Bay was at approximately 14:10 UTC on September 30. The calculated peak surge level was generally consistent with the observed one, with an error of within 20 min. Therefore, the generated peak storm surge could be reproduced with a high accuracy.

The accuracy dropped slightly after the storm surge peak; however, this was attributed to errors in the river flow from the upper river boundary. Observations showed that the water level rose as the flood peak reached the river mouth after the storm surge peak (Fig. 6a; Yokomakura and Touchi). In contrast, the simulated results showed a smaller rise in water level than observed after the storm surge peak and a delay in time. We confirmed the time series of river discharge and attributed this error to the RRI flow input as a lateral boundary condition. Meanwhile, a second peak attributable to the high-water level was noted at 18:00 in the simulated river flow approximately 3 km upstream from the Toyo River estuary (see Fig. 7b; Toyobashi). This phenomenon could not be reproduced by the storm surge model alone; however, it was reproduced with high accuracy by integrating the river flow into the storm surge model.

Next, we investigated the possibility of a compound flood occurrence under Typhoon Trami. Figure 8 shows a time series of water level and discharge in adjacent large-scale rivers and small- and medium-sized rivers in Ise Bay and Mikawa Bay. Nanashima (Shin River), Touchi (Shonai River), and Minami shibata (Tenpaku River) are located on the coast of Ise Bay. Among them, Touchi is in Shonai River, which is a large-scale river as shown in Fig. 8a. Toyobashi (Toyo River), Jinno-shinden (Yagyu River), and Osaki (Umeda River) are in Mikawa Bay. Toyo River is the largest river in Fig. 8b. In Ise Bay, the peak surge level at the estuary appeared at approximately 12:30 to 13:40, 30th Sep., 2018 (Fig. 8a; lower). However, the peak discharge appeared after 15:00, 30th, Sep., 2018 (Fig. 8a; upper), although it varied with the river. The time difference between the storm surge and high river flow peaks was the shortest at Minami shibata at approximately 70 min, followed by Nanashima at 110 min and Touchi at 320 min.

Fig. 8
figure 8

Time series of river discharges (upper) and water-level deviations (lower) based on hindcast experiments of Trami for a Nanashima in the Shin River (medium/small), Touchi in the Shonai River (large), and Minami shibata in the Tenpaku River (medium/small); and b Toyobashi in the Toyo River (large), Jinno-shinden in the Yagyu River (medium/small), and Osaki in the Umeda River (medium/small). Orange vectors indicate the peak time of storm surge, and blue vectors indicate the peak time of river discharge. The right vertical axis is used for a river discharge at the Toyobashi

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In Mikawa Bay, the peak of the storm surge at the river mouth and the peak discharge both appeared at approximately 14:10 (Fig. 8b; lower and upper, respectively), while the peak discharge at Osaki and Maeshiba appeared at approximately 14:40 and 18:10, respectively. The time difference between the storm surge and river flow peaks was the smallest at the Jinno-shinden within 10 min (almost simultaneously), followed by Osaki (approximately 30 min) and Toyobashi (240 min). The water level at the estuary is higher in large rivers compared to small rivers. This is due to the fact that the river discharge entering from the SuWAT boundary is much larger in large rivers than in small rivers, and the converted water level along the river’s upper boundary is also large. On the other hand, the relative flooding risk for the water level is different because of the difference in the level of protection. The ratio of the maximum water level to the embankment height is 45% for the Toyokawa River and 49% for the Yagyu and Umeda Rivers. In the Yagyu and Umeda Rivers, the risk of inundation is increased by the simultaneous occurrence of storm surges and high river flows at the river mouths.

Fortunately, the Trami’s storm surge level was small, at 1.4 m at the Ise Bay and 1.9 m at the Mikawa Bay (the historical maximum storm surge level was over 3 m due to Typhoon Vera (1959)), and compound flooding did not occur. However, in the Tenpaku, Yagyu, and Umeda Rivers, the upstream discharges were also large when the storm surge anomaly at the river mouth was large. Yagyu River had a peak almost simultaneously, suggesting that the probability of co-occurrence of storm surges and high-river flows is extremely high. The time difference between the peak storm surge and maximum river discharge was significant in Shonai and Toyo Rivers, which are large-scale rivers. In contrast, in Yagyu River, the smallest urban river among the target rivers, there was a short time difference between the peak storm surge and river flow. Thus, these findings suggest that the time difference between the maximum level of the storm surge and river flow is strongly positively correlated with the river scale, indicating a potential risk that the storm surge may coincide with high river flow in the estuary of a small-scale river.

4 Sensitivity experiments on peak time difference for storm surge and flooding

Section 3 shows that large-scale rivers have a large difference in the peak time between the storm surge and high river flow, whereas small rivers have a small difference. To verify whether this trend is characteristic of the estuaries of Ise and Mikawa Bays, a series of sensitivity experiments was conducted using Typhoon Hagibis (2019) on multiple tracks using the high-resolution typhoon model (HTM) developed by Yoshino et al. (2012) instead of the WRF. Past cases have shown that the trend of storm surges in Ise Bay and Mikawa Bay was large by typhoons with a northward track (Aichi Pref. Japan, 2021).

4.1 Computational configuration of HTM

Sensitivity experiments for the typhoon track using HTM were originally conducted to evaluate the precipitation distribution and future change in the case of Hagibis hitting the central region of Japan (Yoshino et al. 2021). In the previous study, HTM adequately evaluated the precipitation of Hagibis compared to the observed value using JMA.

In this study, to evaluate the relationship between typhoon tracks and peak times of storm surges and high river flows, we extracted six cases that cause storm surges in Ise Bay and Mikawa Bay from 61 cases identified previously (Yoshino et al. 2021) (Fig. 9). In these experiments, the area around Japan was simulated at 9 km, and that in the Chubu region of Japan was simulated at 3 km. For other detailed simulation setups, please refer to previous studies (Yoshino et al. 2021; Toyoda et al. 2022). The HTM can provide the meteorological fields with high accuracy. Therefore, the precipitation conditions for RRI and the pressure and wind fields for SuWAT were simulated using HTM (15-min intervals). The simulation period was 75 h, including before and after the passage of the typhoon (approximately 55 h before and 20 h after the passage). All six tracks have intensities ranging from 955 to 965 hPa at the time of landfall. The accumulated rainfall was 300 mm in mountainous areas and 100 mm in plain areas (Fig. 10). Using these simulation results, we clarified the compound flood risk by determining the time difference between the storm surge and discharge (ΔT) in each river.

Fig. 9
figure 9

All typhoon tracks of sensitivity experiments for Hagibis in this study. The westernmost case (red) is Track 1, and the easternmost case (blue) is Track 6

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Fig. 10
figure 10

Distributions of cumulative precipitation (75 h) in six cases (Hagibis) and major river lines. a–f correspond to Case 1 to Case 6. The red-colored river line indicates the target rivers

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4.2 Results and discussion of sensitivity experiments

Table 6 summarizes the storm surge and discharge peaks for all cases. Herein, storm surge refers to a storm surge anomaly, ignoring the effect of astronomical tide levels. In addition, the Nagara River and Ibi River have a confluence near their river mouths (Jonan). Similarly, the Gojo River joins the Shin River, represented by “Nanashima,” at its estuary. The yellow-colored cases in the table indicate that the river flow peak did not reach the estuary during the simulation period. Hence, the final time of the simulation period was considered the peak time of the discharge. The red colored number indicates the highest storm surge case and highest river flow case for each river. The Track 3 has the largest storm surge height in all the rivers (Figs. 11 and 12) and has a track passing from the south to the north on the west side of Ise Bay, with the wind-driven effect remarkable in the inner bay. The maximum surge level was 2.95 m at the Minami shibata (Tenpaku River). The maximum storm surges were approximately 2.5 m at Nanashima (Shin River) and Touchi (Shonai River), near the port of Nagoya (Fig. 11). In Mikawa Bay, a storm surge of more than 2 m was generated by the continuous westerly wind (Fig. 12). The storm surge was extremely small at Umenogoh (Nikko River) because the water level gage point was inside the sluice gate of the estuary. The floodgate was implemented as topography, assuming that they were almost closed. Thus, the storm surge was smaller than that at other locations.

Table 6 Results of the sensitivity experiments (storm surge and river discharge) at the estuary points for all rivers. Red indicates the maximum value in six cases for each river, and yellow indicates a case where the river flow peak did not reach the estuary within the simulation period
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Fig. 11
figure 11

Distribution of maximum water-level deviation at the Ise Bay in six cases (Hagibis). Other information corresponds to Fig. 10

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Fig. 12
figure 12

Distribution of maximum water-level deviation at the Mikawa Bay in six cases (Hagibis). Other information corresponds to Fig. 10

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These results indicate that the pathways tending to cause large storm surges in the Ise and Mikawa Bays are similar. However, the peak discharge rate varied with each case and river. As listed in Table 6 and shown in Figs. 11 and 12, the maximum river-water level occurred in Track 3 for Jonan (Ibi River); Track 5 for Yokomakura (Kiso River), Touchi (Shonai River), and Minami shibata (Tenpaku River); Track 4 for Umenogoh (Nikko River), Nanashima (Shin River); and Track 6 for Maeshiba (Toyo River), Jinno-shinden (Yagyu River), and Osaki (Umeda River). The magnitude of river discharge in the estuary varied with the typhoon track because it was affected by both the distribution of precipitation and river size.

Next, the time difference between the peak storm surge and discharge (ΔT) was discussed concerning the river length (RL). Figure 13 indicates that the Kiso River (square), which had the longest RL, tends to have a large ΔT on average, whereas the Shin River (right-pointing triangle), Tenpaku River (left-pointing triangle), Yagyu River (diamond), and Umeda River (hexagon) with smalls RL tend to have a small ΔT. In particular, in Yagyu River, the average ΔT of all six cases is 70 min. Among the ΔTs, the minimum was 15 min. Hence, the impact of the simultaneous occurrence of storm surges and high-river flows was extremely high. The average ΔT was 614.1 min for large-scale rivers and 180.4 min for small- and medium-sized rivers, indicating that high river flows in small and medium-sized rivers reach the river mouth three times faster than those in large-scale rivers. Furthermore, these results suggest that high river flow in large-scale rivers reaches the estuary after the passage of a typhoon because it has a long RL. Meanwhile, high river flow in small- and medium-sized rivers reaches the mouth after the typhoon’s immediate passage from the time of the closest approach of the typhoon. These similar trends are presented in Fig. 14, which were based on the observed values. The correlation coefficient between ΔT and RL is 0.9, indicating a strong positive correlation.

Fig. 13
figure 13

Relationships between the “time difference between the storm surge and discharge at the estuary” and “river length” based on the sensitivity experiments. Color indicates the maximum river discharge rate at the estuary point, and each symbol indicates one river

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Fig. 14
figure 14

Relationship between the “time difference between the storm surge and discharge at the estuary” and “river length” based on the observed values of recent five typhoon cases. Color indicates each typhoon case, and each symbol indicates one river

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In addition, we calculated the standard deviation (normalized) between the ΔT and river extension. The largest standard deviation was found from the Shonai River (triangle) with 0.43, while the smallest was from Yagyu River with 0.31. The average of large-scale rivers (Ibi (circle), Kiso, Shonai, and Toyo (bottom pointing triangle) Rivers) was 0.39, and that of small and medium-sized rivers (Nikko, Shin, Tenpaku, Yagyu, and Umeda Rivers) was 0.36. The standard deviations and ΔT were smaller in small and medium rivers than in large-scale rivers, even when the typhoon tracks were different. The small standard deviations on average indicate that water levels at river mouths tend to be high, regardless of the worst track.

Therefore, appropriate actions (e.g., evacuation) should be taken according to prior typhoon forecasts and real-time river-level information. In addition, water level gages are often not installed at the mouths of small and medium-sized rivers. However, it is necessary to install water level gages and expand the observation network in the future. Note that our results may differ according to the structure of the typhoon and its direction of movement and moving speed. When discussing the compound flooding focused on terms of the temporal scale, we consider ΔT to be an effective indicator. However, the limitation of this discussion is that it lacks sufficient analysis related to the spatial scale of phenomena, such as water level and flow. This study indicates that the impact of the simultaneous occurrence of storm surge and high-river flow at the estuary is greater in smaller rivers. However, in order to determine the compound flooding risk, water level, river discharge, river gradient, and dam operation should be discussed comprehensively.

5 Concluding remarks

The compound flood risk along the estuaries of 11 different-sized rivers in Ise and Mikawa Bays, Japan, was evaluated using an integrated atmosphere–ocean-river model. First, we discussed Typhoon Trami (2018) and accurately estimated the meteorological field, discharge, and storm surge. Second, we set up selected typhoon tracks with similar intensity and precipitation distribution and conducted a series of sensitivity experiments to investigate the simultaneous occurrence of storm surges and high river flow in the estuary. We found a strong positive correlation between the time difference of the storm surge and river flow peaks (ΔT) and the river length (RL). Such a trend was consistent with the observed ΔT. Furthermore, this analysis focused on the time-scale relationship between storm surges and high river flows. As a result, we observed an increased simultaneous occurrence probability of storm surges and high-river flows in small- and medium-sized rivers because ΔT is smaller than that in large rivers. Levee heights are relatively lower in small and medium-sized rivers than in large rivers. Therefore, the exposure is relatively high for a phenomenon of the same scale. Further studies should focus on the spatial scale of compound flooding. The standard deviation of the ΔT between the cases was large for large rivers and small for small- and medium-sized rivers, suggesting that the ΔT is small in the small- and medium-sized rivers, regardless of the typhoon track, and the probability of co-occurrence of storm surge and high-river flow is high.

We used typhoon meteorological fields with relatively little preceding precipitation in the sensitivity experiments. In addition, although this study focused on the simultaneous occurrence of storm surges and high river discharge, it should be noted that the compound flooding risk may be high even when they are not simultaneous, depending on the characteristics of the typhoon or the water system. Therefore, further studies should consider typhoons with different characteristics to obtain a robust compound flooding assessment. Especially, the impact of rainfall ahead of the storm surge should be discussed in further research. Moreover, future climate experiments are required to assess the effect of climate change on compound floods.